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Search: id:A035382
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| A035382 |
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Number of partitions of n into parts congruent to 1 mod 3. |
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+0
4
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| 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 7, 8, 10, 11, 13, 15, 17, 19, 23, 26, 29, 33, 38, 42, 48, 54, 61, 68, 77, 85, 96, 107, 119, 132, 148, 163, 181, 201, 223, 245, 272, 299, 330, 363, 400, 438, 483, 529, 580, 635, 697, 760, 832, 908, 992, 1081, 1180, 1283, 1399, 1521
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n) = A116373(3*n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 15 2006
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FORMULA
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a(n) = 1/n*Sum_{k=1..n} A078181(k)*a(n-k), a(0) = 1.
G.f.=1/product(1-x^(1+3j), j=0..infinity)-1. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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EXAMPLE
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a(9)=4 because we have [7,1,1],[4,4,1],[4,1,1,1,1,1] and [1,1,1,1,1,1,1,1,1].
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MAPLE
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g:=1/product(1-x^(1+3*j), j=0..50)-1: gser:=series(g, x=0, 64): seq(coeff(gser, x, n), n=1..61); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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CROSSREFS
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Cf. A035386, A035451.
Sequence in context: A029075 A029052 A131795 this_sequence A094988 A076269 A143644
Adjacent sequences: A035379 A035380 A035381 this_sequence A035383 A035384 A035385
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KEYWORD
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nonn
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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